Is the email server setting correct? in many cases this can be left blank to use the default php setting in the php.ini.
On some SMTP servers, the From Display Name setting on the From tab needs to be left blank.
Sometimes the email may be trapped in a spam folder. Double check that the email is not being caught as spam.
What is the email address you added on the To tab? is the From email address being pulled from the form? Make sure when testing that you are entering a different email address, some SMTP server will not relay an email where the from and to addresses are the same .
If all else fails, contact the host to see if they can look at the SMTP server error logs to see why the email is not being relayed by the SMTP server.